Monson was elected Utah State Auditor in 1972. He was only one of two Republicans to win a statewide office that year, the rest being taken by the Democrats.[2] He served from 1973 to 1977. He then served as lieutenant governor of Utah for two terms, from 1977 to 1985.

In 1984, Monson ran for the United States House of Representatives for the Ninety-ninth Congress. He had a surprisingly difficult race that year. In the general election, he defeated former state Senator Frances Farley by a vote of 105,540 to 105,044.[3] He was not a candidate for reelection in 1986, ending his political career in January 3, 1987 after serving only one term as a representative. He subsequently became a business executive involved in international trade and recycling paper. He currently resides in Salt Lake City.